Apparently the faucets drips are not the hot water side or you would have hot water a lot faster. It takes a while because you have to displace the cold water in the pipe. The larger the pipe, the longer the pipe, and the slower the water flows from the faucet, the longer it will take to get hot water.

In my old apartment, they ran PEX pipe underneith the apartment, in the crawl space. Come wintertime, when it got cold, the water was freezing and took forever to warm up. Found a leak one day, landlord wouldn't get to it, so I had to take care of it. Well, when I opened up the wall I found that there was like a bazillion (that's a lot) feet of the pipe just coiled up down there. That's why it was taking so long for hot water.... Just because your faucet is 15 feet away doesn't mean there is 15feet of pipe between here and there.